Question: $h(t) = -7+f(t)$ $g(t) = -4t$ $f(t) = -4t-2-4(g(t))$ $ g(h(7)) = {?} $
First, let's solve for the value of the inner function, $h(7)$ . Then we'll know what to plug into the outer function. $h(7) = -7+f(7)$ To solve for the value of $h$ , we need to solve for the value of $f(7)$ $f(7) = (-4)(7)-2-4(g(7))$ To solve for the value of $f$ , we need to solve for the value of $g(7)$ $g(7) = (-4)(7)$ $g(7) = -28$ That means $f(7) = (-4)(7)-2+(-4)(-28)$ $f(7) = 82$ That means $h(7) = -7+82$ $h(7) = 75$ Now we know that $h(7) = 75$ . Let's solve for $g(h(7))$ , which is $g(75)$ $g(75) = (-4)(75)$ $g(75) = -300$